If (1, a), (a, 1), and (a-1, a-1) are co-linear, then we must have (a-1)/(1- a)= -1 (the slope of the line from (1,a) to (a,1)) equal to (a-1-a/ a-1-1)= -1/a (the slope of the line from (a, 1) to (a-1, a-1)). -1= -1/a is satisfied only by a= 1. But if a= 1, (1, a)= (1, 1)= (a, 1) so the three points are not distinct.

There is NO value of a that will make these points distinct and collinear.

If (1, a), (a, 1), and (a-1, a-1) are co-linear, then we must have (a-1)/(1- a)= -1 (the slope of the line from (1,a) to (a,1)) equal to (a-1-a/ a-1-1)= -1/a (the slope of the line from (a, 1) to (a-1, a-1)). -1= -1/a is satisfied only by a= 1. But if a= 1, (1, a)= (1, 1)= (a, 1) so the three points are not distinct.

There is NO value of a that will make these points distinct and collinear.